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I’m implementing a code to solve the equation of motion using the 4-step Adams-Bashforth method.

Here’s my section of code that does this:

a=F/m;

upnew= up + delta *( (55/24)*a - (59/24)*am1 +(37/24)*am2 - (3/8)*am3 );

xnew=x + delta *( (55/24)*up - (59/24)*upm1 +(37/24)*upm2 - (3/8)*upm3);

am1=a;

am2=am1;

am3=am2;

upm1=up;

upm2=upm1;

upm3=upm2;

up=upnew;

x=xnew;

It seems to work; at least it produces sensible results which agree with the Euler forwards method. However, I read that the global error should be proportional to delta^4, but this code produces results that have errors proportional to delta. Why is this? Is there some quirk of using the method as a double integral reduces the accuracy? Or am I getting something wrong?

Thanks in advance,

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# Global Errors when solving the Equation of Motion

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